Exercise 6 Page 97

Practice makes perfect

When dividing powers with the same base, we can simplify this by rewriting it as a single power with the same base, and where the exponent is the difference of the exponent in the numerator and the denominator.

h^9/h^(11)

DivPow

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

h^(9-11)

SubTerm

Subtract term

h^(- 2)

When we multiply powers with the same base, we can simplify this by rewriting it as a single power with the same base, and where the exponent is the sum of the exponents.

x^3* x^4

MultPow

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

x^(3+4)

AddTerms

Add terms

x^7

When we have a power inside a power, we can multiply the exponents.

(3k^5)^2

PowProdII

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

3^2(k^5)^2

CalcPow

Calculate power

9(k^5)^2

PowPow

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

9k^(5* 2)

Multiply

9k^(10)

When we multiply powers with the same base we can simplify this by rewriting it as a single power with the same base, and where the exponent is the sum of the exponents. Note that any number can be rewritten as a number raised to the power of 1.

n^7* n

MultBasePow

a*a^m=a^(1+m)

n^(7+1)

AddTerms

Add terms

n^8

Let's simplify the expression using the same rules as we did in previous parts.

16x^4y^3/2x^4

ReduceFrac

a/b=.a /x^4./.b /x^4.

16y^3/2