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UPTET Paper 1 Model Test 1

Section: Mathematics

Question : 98 of 150

Marks: +1, -0

((64)^{\frac{2}{3}})^{\frac{1}{2}}

Solution:

Concept:

When a power is raised to another power, we multiply the exponents:

(a^m)^n = a^{m \times n}

Explanation:

Start with the given expression:

((64)^{\frac{2}{3}})^{\frac{1}{2}}

Apply the exponent rule: multiply the exponents

\frac{2}{3}

and

\frac{1}{2}

\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}

So the expression becomes

64^{\frac{1}{3}}

, which is the cube root of 64.

Since

64 = 4^3

, we have

64^{\frac{1}{3}} = (4^3)^{\frac{1}{3}} = 4^{3 \times \frac{1}{3}} = 4^1 = 4

Thus, the value of

((64)^{\frac{2}{3}})^{\frac{1}{2}}

is 4.

Answer:

C. 04

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