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EXPONENTS and POWERS

296374 Which expression is equivalent to 81?

1

2^{9}

2

(\frac{1}{3})^{- 4}

3

3^{- 4}

4

(\frac{1}{3})^{4}

Explanation:

$(\frac{1}{3})^{- 4}$
$(\frac{1}{3})^{- 4} = 3^{4} = 81$

EXPONENTS and POWERS

296375 Mark $(✓)$ tick against the correct answer in the following:
${(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3} = ?$

1

\frac{19}{64}

2

\frac{64}{19}

3

\frac{27}{16}

4 None of these.

Explanation:

$\frac{19}{64}$
$∵ {(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3}$
$= [(3)^{3} - (2)^{3}] \div (4)^{3}$
$= (27 - 8) \div 64$
$= 19 \div 64 = \frac{19}{64}$

EXPONENTS and POWERS

296376 The expanded form of a $^{1}$ is:

1 a × 6

2 a × a × a × a × a × a

3 a × a × a × a

4 a + a + a + a + a + a

Explanation:

a × a × a × a × a × a
a $^{1}$ = a × a × a × a × a × a

EXPONENTS and POWERS

296377 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: product of powers property
Reason: 5 $^{1}$ × 5 $^{1}$ = 5 $^{1}$

1 Both assertion and reason are correct and reason is correct explanation for assertion.

2 Both assertion and reason are correct but reason is correct explanation for assertion.

3 Assertion is correct but reason is false.

4 Both assertion and reason are false.

EXPONENTS and POWERS

296378 Mark $(✓)$ against the correct answer in the following:
$(\frac{- 3}{4})^{- 3} = ?$

1

\frac{27}{64}

2

\frac{64}{27}

3

\frac{- 27}{64}

4

\frac{- 64}{27}

Explanation:

$\frac{- 64}{27}$
$(\frac{- 3}{4})^{- 3} = (\frac{4}{- 3})^{3}$ $[Since (\frac{a}{b})^{- n} = (\frac{b}{a})^{n}]$
$= \frac{4^{3}}{(- 3)^{3}}$
$= \frac{4 \times 4 \times 4}{(- 3) \times (- 3) \times (- 3)} = \frac{64}{(- 27)}$
$= \frac{64 \times - 1}{- 27 \times - 1} = \frac{- 64}{27}$

EXPONENTS and POWERS

296374 Which expression is equivalent to 81?

1

2^{9}

2

(\frac{1}{3})^{- 4}

3

3^{- 4}

4

(\frac{1}{3})^{4}

Explanation:

$(\frac{1}{3})^{- 4}$
$(\frac{1}{3})^{- 4} = 3^{4} = 81$

EXPONENTS and POWERS

296375 Mark $(✓)$ tick against the correct answer in the following:
${(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3} = ?$

1

\frac{19}{64}

2

\frac{64}{19}

3

\frac{27}{16}

4 None of these.

Explanation:

$\frac{19}{64}$
$∵ {(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3}$
$= [(3)^{3} - (2)^{3}] \div (4)^{3}$
$= (27 - 8) \div 64$
$= 19 \div 64 = \frac{19}{64}$

EXPONENTS and POWERS

296376 The expanded form of a $^{1}$ is:

1 a × 6

2 a × a × a × a × a × a

3 a × a × a × a

4 a + a + a + a + a + a

Explanation:

a × a × a × a × a × a
a $^{1}$ = a × a × a × a × a × a

EXPONENTS and POWERS

296377 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: product of powers property
Reason: 5 $^{1}$ × 5 $^{1}$ = 5 $^{1}$

1 Both assertion and reason are correct and reason is correct explanation for assertion.

2 Both assertion and reason are correct but reason is correct explanation for assertion.

3 Assertion is correct but reason is false.

4 Both assertion and reason are false.

EXPONENTS and POWERS

296378 Mark $(✓)$ against the correct answer in the following:
$(\frac{- 3}{4})^{- 3} = ?$

1

\frac{27}{64}

2

\frac{64}{27}

3

\frac{- 27}{64}

4

\frac{- 64}{27}

Explanation:

$\frac{- 64}{27}$
$(\frac{- 3}{4})^{- 3} = (\frac{4}{- 3})^{3}$ $[Since (\frac{a}{b})^{- n} = (\frac{b}{a})^{n}]$
$= \frac{4^{3}}{(- 3)^{3}}$
$= \frac{4 \times 4 \times 4}{(- 3) \times (- 3) \times (- 3)} = \frac{64}{(- 27)}$
$= \frac{64 \times - 1}{- 27 \times - 1} = \frac{- 64}{27}$

EXPONENTS and POWERS

296374 Which expression is equivalent to 81?

1

2^{9}

2

(\frac{1}{3})^{- 4}

3

3^{- 4}

4

(\frac{1}{3})^{4}

Explanation:

$(\frac{1}{3})^{- 4}$
$(\frac{1}{3})^{- 4} = 3^{4} = 81$

EXPONENTS and POWERS

296375 Mark $(✓)$ tick against the correct answer in the following:
${(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3} = ?$

1

\frac{19}{64}

2

\frac{64}{19}

3

\frac{27}{16}

4 None of these.

Explanation:

$\frac{19}{64}$
$∵ {(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3}$
$= [(3)^{3} - (2)^{3}] \div (4)^{3}$
$= (27 - 8) \div 64$
$= 19 \div 64 = \frac{19}{64}$

EXPONENTS and POWERS

296376 The expanded form of a $^{1}$ is:

1 a × 6

2 a × a × a × a × a × a

3 a × a × a × a

4 a + a + a + a + a + a

Explanation:

a × a × a × a × a × a
a $^{1}$ = a × a × a × a × a × a

EXPONENTS and POWERS

296377 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: product of powers property
Reason: 5 $^{1}$ × 5 $^{1}$ = 5 $^{1}$

1 Both assertion and reason are correct and reason is correct explanation for assertion.

2 Both assertion and reason are correct but reason is correct explanation for assertion.

3 Assertion is correct but reason is false.

4 Both assertion and reason are false.

EXPONENTS and POWERS

296378 Mark $(✓)$ against the correct answer in the following:
$(\frac{- 3}{4})^{- 3} = ?$

1

\frac{27}{64}

2

\frac{64}{27}

3

\frac{- 27}{64}

4

\frac{- 64}{27}

Explanation:

$\frac{- 64}{27}$
$(\frac{- 3}{4})^{- 3} = (\frac{4}{- 3})^{3}$ $[Since (\frac{a}{b})^{- n} = (\frac{b}{a})^{n}]$
$= \frac{4^{3}}{(- 3)^{3}}$
$= \frac{4 \times 4 \times 4}{(- 3) \times (- 3) \times (- 3)} = \frac{64}{(- 27)}$
$= \frac{64 \times - 1}{- 27 \times - 1} = \frac{- 64}{27}$

EXPONENTS and POWERS

296374 Which expression is equivalent to 81?

1

2^{9}

2

(\frac{1}{3})^{- 4}

3

3^{- 4}

4

(\frac{1}{3})^{4}

Explanation:

$(\frac{1}{3})^{- 4}$
$(\frac{1}{3})^{- 4} = 3^{4} = 81$

EXPONENTS and POWERS

296375 Mark $(✓)$ tick against the correct answer in the following:
${(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3} = ?$

1

\frac{19}{64}

2

\frac{64}{19}

3

\frac{27}{16}

4 None of these.

Explanation:

$\frac{19}{64}$
$∵ {(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3}$
$= [(3)^{3} - (2)^{3}] \div (4)^{3}$
$= (27 - 8) \div 64$
$= 19 \div 64 = \frac{19}{64}$

EXPONENTS and POWERS

296376 The expanded form of a $^{1}$ is:

1 a × 6

2 a × a × a × a × a × a

3 a × a × a × a

4 a + a + a + a + a + a

Explanation:

a × a × a × a × a × a
a $^{1}$ = a × a × a × a × a × a

EXPONENTS and POWERS

296377 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: product of powers property
Reason: 5 $^{1}$ × 5 $^{1}$ = 5 $^{1}$

1 Both assertion and reason are correct and reason is correct explanation for assertion.

2 Both assertion and reason are correct but reason is correct explanation for assertion.

3 Assertion is correct but reason is false.

4 Both assertion and reason are false.

EXPONENTS and POWERS

296378 Mark $(✓)$ against the correct answer in the following:
$(\frac{- 3}{4})^{- 3} = ?$

1

\frac{27}{64}

2

\frac{64}{27}

3

\frac{- 27}{64}

4

\frac{- 64}{27}

Explanation:

$\frac{- 64}{27}$
$(\frac{- 3}{4})^{- 3} = (\frac{4}{- 3})^{3}$ $[Since (\frac{a}{b})^{- n} = (\frac{b}{a})^{n}]$
$= \frac{4^{3}}{(- 3)^{3}}$
$= \frac{4 \times 4 \times 4}{(- 3) \times (- 3) \times (- 3)} = \frac{64}{(- 27)}$
$= \frac{64 \times - 1}{- 27 \times - 1} = \frac{- 64}{27}$

EXPONENTS and POWERS

296374 Which expression is equivalent to 81?

1

2^{9}

2

(\frac{1}{3})^{- 4}

3

3^{- 4}

4

(\frac{1}{3})^{4}

Explanation:

$(\frac{1}{3})^{- 4}$
$(\frac{1}{3})^{- 4} = 3^{4} = 81$

EXPONENTS and POWERS

296375 Mark $(✓)$ tick against the correct answer in the following:
${(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3} = ?$

1

\frac{19}{64}

2

\frac{64}{19}

3

\frac{27}{16}

4 None of these.

Explanation:

$\frac{19}{64}$
$∵ {(\frac{1}{2})^{- 3} - (\frac{1}{2})^{- 3}} \div (\frac{1}{4})^{- 3}$
$= [(3)^{3} - (2)^{3}] \div (4)^{3}$
$= (27 - 8) \div 64$
$= 19 \div 64 = \frac{19}{64}$

EXPONENTS and POWERS

296376 The expanded form of a $^{1}$ is:

1 a × 6

2 a × a × a × a × a × a

3 a × a × a × a

4 a + a + a + a + a + a

Explanation:

a × a × a × a × a × a
a $^{1}$ = a × a × a × a × a × a

EXPONENTS and POWERS

296377 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: product of powers property
Reason: 5 $^{1}$ × 5 $^{1}$ = 5 $^{1}$

1 Both assertion and reason are correct and reason is correct explanation for assertion.

2 Both assertion and reason are correct but reason is correct explanation for assertion.

3 Assertion is correct but reason is false.

4 Both assertion and reason are false.

EXPONENTS and POWERS

296378 Mark $(✓)$ against the correct answer in the following:
$(\frac{- 3}{4})^{- 3} = ?$

1

\frac{27}{64}

2

\frac{64}{27}

3

\frac{- 27}{64}

4

\frac{- 64}{27}

Explanation:

$\frac{- 64}{27}$
$(\frac{- 3}{4})^{- 3} = (\frac{4}{- 3})^{3}$ $[Since (\frac{a}{b})^{- n} = (\frac{b}{a})^{n}]$
$= \frac{4^{3}}{(- 3)^{3}}$
$= \frac{4 \times 4 \times 4}{(- 3) \times (- 3) \times (- 3)} = \frac{64}{(- 27)}$
$= \frac{64 \times - 1}{- 27 \times - 1} = \frac{- 64}{27}$

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