Question

Simplify the expression (6^4)^2

Answer 1

`\boxed{ \purple{ {6}^(8) }}`

Explanation:

`\mathsf{ ( { {6}^(4)) }^(2) }`

It is the example of Power to power law of indices.

Multiply the exponents

⇒
`\mathsf{ {6}^(4 * 2) }`

Multiply the numbers

⇒
`\mathsf{ {6}^(8) }`

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`\mathsf{\orange{ \underline{ power \: to \: power \: law \: of \: indices}}}`

If
`\mathsf{ ({x}^(a) )^(b)}` is an algebraic term then
`\mathsf{( {x}^(a) ) ^(b) = {x}^(a * b) }`

i.e When an algebraic term in the index form is raised to another index , the base is raised to the power of two indices.

Hope I helped!

Best regards!!

Answer 2

When raising a power inside parentheses to another power, multiply the numbers:

(6^4)^2 = 6^(4x2) = 6^8

Simplified = 6^8

6^8 = 1679616