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The value of \( \Large \left(243\right) ^{0.16} \times \left(243\right)^{0.04} \) is equal to:

A) 0.16
B) 3
C) \( \Large \frac{1}{3} \)
D) 0.04

Correct Answer:


B) 3

Description for Correct answer:
\( \Large \left(243\right) ^{0.16} \times \left(243\right)^{0.04} \)

=\( \Large 243^{0.16+0.04} \left[ a^{m} \times b^{n}=a^{m+n} \right]\)

=\( \Large 243^{0.20} \)

=\( \Large 243^{\frac{20}{100}} = 243^{\frac{1}{5}}\)

=\( \Large \sqrt[5]{243} =3\)

Part of solved Indices and Surd questions and answers : >> Elementary Mathematics >> Indices and Surd

Comments

Similar Questions

1). The value of \( \Large \left(256\right) ^{0.16} \times \left(256\right)^{0.09} \) is:

A). 256.25

B). 64

C). 16

D). 4

2). The simplification of \( \Large \frac{0.06 \times 0.06 \times 0.06-0.05 \times 0.05 \times 0.05}{0.06 \times 0.06+0.06 \times 0.05+0.05 \times 0.05} \)

A). 1

B). 0.1

C). 0.01

D). 0.001

3). Simplify \( \Large \frac{0.05 \times 0.05 \times 0.05-0.04 \times 0.04 \times 0.04}{0.05 \times 0.05+0.002+0.04 \times 0.04} \)

A). 1

B). 0.1

C). 0.01

D). 0.001

4). Simplify \( \Large \frac{5.32 \times 56+5.32 \times 44 }{ \left(7.66^{2}\right)- \left(2.34\right)^{2} } \)

A). 7.2

B). 8.5

C). 10

D). 12

5). Which one of the following is least?\( \Large \sqrt{3},\sqrt[3]{2},\sqrt{2},\sqrt[3]{4} \)

A). \( \Large \sqrt{2} \)

B). \( \Large \sqrt[3]{2} \)

C). \( \Large \sqrt{3} \)

D). \( \Large \sqrt[3]{4} \)

6). Which one of the following is biggest?\( \Large \sqrt[3]{4},\sqrt[4]{6},\sqrt[6]{15},\sqrt[12]{245} \)

A). \( \Large \sqrt[3]{4} \)

B). \( \Large \sqrt[4]{6} \)

C). \( \Large \sqrt[6]{15} \)

D). \( \Large \sqrt[12]{245} \)

7). Simplify:\( \Large \left[ \sqrt[3]{\sqrt[6]{5^{9}}} \right]^{4}\left[ \sqrt[3]{\sqrt[6]{5^{9}}} \right]^{4} \)

A). \( \Large 5^{2} \)

B). \( \Large 5^{4} \)

C). \( \Large 5^{8} \)

D). \( \Large 5^{12} \)

8). If \( \Large 27^{2n-1}= \left(243\right)^{3} \) then the value of n is:

A). 3

B). 6

C). 7

D). 9

9). If \( \Large 3^{x+8}=27^{2x+1} \) then value of x is:

A). 7

B). 3

C). -2

D). 1

10). \( \Large \left(\sqrt{8}-\sqrt{4}-\sqrt{2}\right) \) equales:

A). \( \Large 2-\sqrt{2} \)

B). \( \Large \sqrt{2}-2 \)

C). 2

D). -2