Choose the correct word/answer and fill in the blanks:
${(100^{2})}^{3}$ and ${[100^{3}]}^{2}$ are _________ (same/different)

Open in App

Solution

By the properties of exponent, we know that -
${(a^{x})}^{y} = a^{x \times y}$
By using the above property -
${(100^{2})}^{3} = 100^{2 \times 3} = 100^{6} {(100^{3})}^{2} = 100^{3 \times 2} = 100^{6}$
Since, ${(100^{2})}^{3}$ and ${[100^{3}]}^{2}$ are having the same exponent and base, so they will have the same value,
therefore, the correct answer is same.

Suggest Corrections

Similar questions

Choose the correct word/answer and fill in the blanks:

$2^{3}$ and ${(3)}^{2}$ are _________ (same/different)

Choose the correct word/answer and fill in the blanks:

${(2^{100})}^{0}$ and $1^{100}$ are _________ (same/different)

Choose the correct word/answer and fill in the blanks:

${(4^{3})}^{2}$ and ${(4^{2})}^{3}$ are _________ (same/different)

Choose the correct word/answer and fill in the blanks:

$5^{0}$ and ${(1000)}^{0}$ are _________ (same/different)

Choose the correct word/answer and fill in the blanks:

${(- 1)}^{11}$ and $1^{11}$ are _________ (same/different)

Join BYJU'S Learning Program