Simplify ((2^10)^3*2^-10)/(2^-7)

$\frac{{(2^{10})}^{3} \cdot 2^{- 10}}{2^{- 7}}$

Step 1

Move $2^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(2^{10})}^{3}}{2^{- 7} \cdot 2^{10}}$

Step 2

Multiply $2^{- 7}$ by $2^{10}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(2^{10})}^{3}}{2^{- 7 + 10}}$

Add $- 7$ and $10$ .

$\frac{{(2^{10})}^{3}}{2^{3}}$

Step 3

Simplify the numerator.

Multiply the exponents in ${(2^{10})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2^{10 \cdot 3}}{2^{3}}$

Multiply $10$ by $3$ .

$\frac{2^{30}}{2^{3}}$

Raise $2$ to the power of $30$ .

$\frac{1073741824}{2^{3}}$

Step 4

Simplify the expression.

Raise $2$ to the power of $3$ .

$\frac{1073741824}{8}$

Divide $1073741824$ by $8$ .

$134217728$