Exercise 68 Page 644

We want to simplify the given expression. We can see that our expression is the division of two expressions: |-4^7| and 3^34^(-2) + 4^3sqrt(16). To simplify the given expression, we can start by simplifying the divisor of the given expression, remembering about the order of operations and using the Properties of Exponents.

3^3/4^(-2) + 4^3/sqrt(16)

CalcRoot

Calculate root

3^3/4^(-2) + 4^3/4

DivPow

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

3^3/4^(-2) + 4^2

FracToMultNegExponent

a/b^m=ab^(- m)

3^3 * 4^(-(-2)) + 4^2

NegNeg

- (- a)=a

3^3 * 4^2 + 4^2

CalcPow

Calculate power

27 * 16 + 16

Multiply

Multiply

432 + 16

AddTerms

Add terms

448

We can now substitute the received value for the given expression and simplify it.

|-4^7| ÷ (3^3/4^(-2) + 4^3/sqrt(16))

Substitute

3^3/4^(-2) + 4^3/sqrt(16)= 448

|-4^7| ÷ 448

DivToFrac

a÷ b=a/b

|-4^7|/448

AbsNeg

|-4^7|=4^7

4^7/448

UseCalc

Use a calculator

36.571428 ...

RoundDec

Round to 1 decimal place(s)

36.6