Question

practice problems

1. evaluate.

a. $(-10)^0$
b. $\frac{10^3}{10^3}$
c. $-10^2 + 10^1 + 10^0$

Explanation:

Part a

Step1: Recall the zero - exponent rule

Any non - zero number raised to the power of 0 is 1. The base here is \(- 10\), and \(-10
eq0\).
So, \((-10)^{0}=1\)

Step1: Recall the quotient rule for exponents

The quotient rule for exponents states that \(\frac{a^{m}}{a^{n}}=a^{m - n}\) when \(a
eq0\). Here, \(a = 10\), \(m = 3\) and \(n = 3\).
So, \(\frac{10^{3}}{10^{3}}=10^{3-3}\)

Step2: Simplify the exponent

\(10^{3 - 3}=10^{0}\)

Step3: Apply the zero - exponent rule

Since \(10
eq0\), \(10^{0}=1\)

Step1: Evaluate each term

• For the first term \(-10^{2}\): Remember that \(10^{2}=10\times10 = 100\), so \(-10^{2}=- 100\)
• For the second term \(10^{1}\): By the definition of exponents, \(10^{1}=10\)
• For the third term \(10^{0}\): By the zero - exponent rule, \(10^{0}=1\)

Step2: Combine the terms

\(-10^{2}+10^{1}+10^{0}=-100 + 10+1\)
First, \(-100+10=-90\), then \(-90 + 1=-89\)

Answer:

\(1\)

Part b