Simplify the expression to a form in which 2 is raised to a single integer power. fraction numerator open parentheses 2 to the power of 10 close parentheses cubed 2 to the power of short dash 10 end exponent over denominator 2 to the power of short dash 7 end exponent end fraction

Answer:

2^27

Step-by-step explanation:

Given the following expression:

[(2^10)^3 x (2^-10)] ÷ 2^-7

This can be easily simplified. Let us simplify the numerator first. To do that, we have

(2^10)^3 making use of the power rule of indices that says:

(A^a)^b = A^ab where a and b are powers, we have:

2^(10x3) = 2^30

Therefore the numerator becomes:

2^30 x 2^-10. Also making use of the multiplication rule that says:

A^a x A^b = A^(a + b), we have

2^30 x 2^-10 = 2^(30 – 10) = 2^20.

Now we have:

(2^20) ÷ (2^-7)

To simplify this, we need the division rule of indices which says:

A^a ÷ A^b = A^(a – b)

Therefore we have:

(2^20) ÷ (2^-7) = 2^[20 – (–7)] = 2^(20+7) = 2^27

Following are the solution to the given expression:

Given:

[tex]\to \frac{[(2^{10})^3 \times (2^{-10})]}{2^{-7}}[/tex]

To find:

value=?

Solution:

[tex]\to \frac{[(2^{10})^3 \times (2^{-10})]}{2^{-7}}[/tex]

Using formula:

[tex]\to (A^a)^b = A^{ab}\\\\\to A^a \div A^b = A^{(a - b)}[/tex]

Solve the equation:

[tex]\to \frac{[(2^{30}) \times (2^{-10})]}{2^{-7}} \\\\\to \frac{(2^{30})}{2^{-7}} \times \frac{(2^{-10})}{2^{-7}} \\\\ \to \frac{(2^{30})}{2^{-7}} \times \frac{(2^{-10})}{2^{-7}} \\\\\to (2^{30 - (-7)}) \times (2^{-10- (-7)}) \\\\\to 2^{37} \times 2^{-3} \\\\\to 2^{37 -3} \\\\\to 2^{34} \\\\[/tex]

Therefore, the final answer is "[tex]\bold{2^{34}}[/tex]".

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