Exercise 95 Page 368

Practice makes perfect

Let's consider the given expression. 3^5/3^(10) We want to simplify the expression. Let's use the Quotient of Powers Law. This law states that to divide powers with the same base, we can subtract their exponents.

3^5/3^(10)

DivPow

a^m/a^n= a^(m-n)

3^(5-10)

SubTerm

Subtract term

3^(- 5)

To give the answer without negative exponents, we will use the Negative Exponent Property.

Negative Exponent Property
a^(- n)= 1a^n, for every nonzero number a

Let's rewrite our expression using this property.

3^(- 5)

NegOneExponentToFrac

a^(- 1)=1/a

1/3^5

We want to simplify the following expression. 10x^4(10x)^(- 2) Let's start by rewriting (10x)^(- 2) using the Negative Exponent Property.

10x^4(10x)^(- 2)

NegExponentToFrac

a^(- m)=1/a^m

10x^4* 1/(10x)^2

Next, we will simplify the fraction using the Power of a Product Law. This law states that if we want to calculate the power of a product, we distribute the power to each factor and then multiply.

10x^4* 1/(10x)^2

PowProdII

(a b)^m=a^m b^m

10x^4* 1/10^2 x^2

Now we will continue simplifying using the Quotient of Powers Law and the Negative Exponent Property.

10x^4* 1/10^2 x^2

MoveLeftFacToNumOne

a* 1/b= a/b

10x^4/10^2 x^2

WriteProdFrac

Write as a product of fractions

10/10^2* x^4/x^2

a=a^1

10^1/10^2* x^4/x^2

DivPow

a^m/a^n= a^(m-n)

10^(1-2)* x^(4-2)

SubTerms

Subtract terms

10^(- 1)* x^2

NegOneExponentToFrac

a^(- 1)=1/a

1/10 * x^2

MoveRightFacToNumOne

1/b* a = a/b

x^2/10

Let's consider the given expression. (1/4)^3* (4)^2 We want to simplify the expression. Let's start by rewriting ( 14)^3 using the Negative Exponent Property.

(1/4)^3* (4)^2

FracToNegExponent

1/a^m=a^(- m)

4^(- 3)* 4^2

Next, we will use the Product of Powers Law. Recall that the Product of Powers Law states that to multiply powers with the same base, we can add their exponents.

4^(- 3)* 4^2

MultPow

a^m*a^n=a^(m+n)

4^(- 3+2)

AddTerms

Add terms

4^(- 1)

Finally, we will use once again the Negative Exponent Property to write our answer without negative exponents.

4^(- 1)

NegOneExponentToFrac

a^(- 1)=1/a

1/4