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Chapter 2: Problem 1

Evaluate the given expression. Do not use a calculator. $$ 2^{5}-5^{2} $$

Short Answer

Expert verified
The given expression \(2^5 - 5^2\) can be simplified as follows: Compute each term separately, \(2^5 = 32\) and \(5^2 = 25\). Then subtract the second term from the first term, resulting in \(32 - 25 = 7\). Therefore, the simplified expression is 7.

Step by step solution

01

Compute the first term

To compute the first term \(2^5\), we need to raise the base, 2, to the 5th power. This means we should multiply 2 by itself four more times: \(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\).
02

Compute the second term

To compute the second term \(5^2\), we need to raise the base, 5, to the 2nd power. This means we should multiply 5 by itself once: \(5^2 = 5 \times 5 = 25\).
03

Perform the subtraction

Now we subtract the second term (25) from the first term (32): \(2^5 - 5^2 = 32 - 25 = 7\). So, the given expression is equal to 7 when simplified.

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Most popular questions from this chapter

Give an example of polynomials \(p\) and \(q\) of degree 3 such that \(p(1)=q(1), p(2)=q(2),\) and \(p(3)=q(3),\) but \(p(4) \neq q(4)\).

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Write the indicated expression as a ratio of polynomials, assuming that $$ r(x)=\frac{3 x+4}{x^{2}+1}, \quad s(x)=\frac{x^{2}+2}{2 x-1}, \quad t(x)=\frac{5}{4 x^{3}+3} $$. $$ (3 r-2 s)(x) $$
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