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Repeated Exponentiation

If a is an in...

Question

If $a$ is an integer other than zero, $p$ and $q$ are integers, then the value of $(a^{p})^{q}$ is for $a = 2$ , $p = 3$ and $q = 4$ ?

2^{7}

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2^{12}

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2^{81}

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2^{34}

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Solution

The correct option is B $2^{12}$
Given that,
$a = 2, p = 3, q = 4$
Now,
$(a^{p})^{q} = a^{p \times q}$
If we put the given values of $a$ , $p$ and $q$ into $(a^{p})^{q}$ , we get
$\Rightarrow (a^{p})^{q} = a^{p \times q}$
$\Rightarrow (2^{3})^{4} = 2^{3 \times 4}$
$= 2^{12}$

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If a is an integer other than zero, p and q are integers, then the value of (ap)q is for a=2, p=3 and q=4?

The correct option is B 212Given that, a=2,p=3,q=4 Now, (ap)q=ap×q If we put the given values of a, p and q into (ap)q, we get ⇒(ap)q=ap×q ⇒(23)4=23×4 =212

If $a$ is an integer other than zero, $p$ and $q$ are integers, then the value of $(a^{p})^{q}$ is for $a = 2$ , $p = 3$ and $q = 4$ ?

The correct option is B $2^{12}$
Given that,
$a = 2, p = 3, q = 4$
Now,
$(a^{p})^{q} = a^{p \times q}$
If we put the given values of $a$ , $p$ and $q$ into $(a^{p})^{q}$ , we get
$\Rightarrow (a^{p})^{q} = a^{p \times q}$
$\Rightarrow (2^{3})^{4} = 2^{3 \times 4}$
$= 2^{12}$