Exercise 132 Page &nbsp; 437

15+1/5* 7/4

Add terms

16/5* 7/4

Now we can multiply the fractions and write the result as a mixed number in simplest form.

16/5* 7/4

16* 7/5* 4

112/20

ReduceFrac

a/b=.a /4./.b /4.

112÷ 4/20÷ 4

Calculate quotient

28/5

▼

Write fraction as a mixed number

WriteSum

Write as a sum

25+3/5

WriteSumFrac

Write as a sum of fractions

25/5+3/5

Calculate quotient

5+3/5

Add terms

5 35

Let's consider the given expression. 5^3* ( - 4/5) We want to simplify the expression. According to the Order of Operations, we need to start by calculating the power. Then, we will perform the multiplication.

5^3* ( - 4/5)

Calculate power

125* ( - 4/5)

MultPosNeg

a(- b)=- a * b

- 125 * 4/5

MoveLeftFacToNum

a*b/c= a* b/c

- 125 * 4/5

- 500/5

Calculate quotient

- 100

We are asked to simplify the given expression. 2^4* 5/8 According to the Order of Operations, we need to start by calculating the power and then we will perform the multiplication.

2^4* 5/8

Calculate power

16* 5/8

MoveLeftFacToNum

a*b/c= a* b/c

16* 5/8

80/8

Calculate quotient

Let's consider the given expression. - 1/2* 3^2 Like in Part B and Part C, to simplify the expression, we need to start by calculating the power. Then, we will perform the multiplication.

- 1/2* 3^2

Calculate power

- 1/2* 9

MoveRightFacToNumOne

1/b* a = a/b

- 9/2

The expression is equal to - 92. We can write this fraction as a mixed number.

- 9/2

▼

Write fraction as a mixed number

WriteSum

Write as a sum

- 8+1/2

WriteSumFrac

Write as a sum of fractions

- (8/2+1/2)

Calculate quotient

- (4+1/2)

Add terms

- 4 12

We want to simplify the following expression. - 5/6+(1/2)^2 According to the Order of Operations, we need to start by calculate the power. To do this, we can use the Power of a Quotient Law. This law states that if we want to calculate the power of a quotient, we can write the quotient as the ratio of two powers with the same exponent.

- 5/6+(1/2)^2

PowQuot

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

- 5/6+1^2/2^2

Calculate power

- 5/6+1/4

Now let's add the fractions and write the result in simplest form.

- 5/6+1/4

a/b=a * 4/b * 4

- 5* 4/6* 4+1/4

- 20/24+1/4

a/b=a * 6/b * 6

- 20/24+1* 6/4* 6

- 20/24+6/24

MoveNegFracToNum

Put minus sign in numerator

- 20/24+6/24

AddFrac

Add fractions

- 20+6/24

Add terms

- 14/24

MoveNegNumToFrac

Put minus sign in front of fraction

- 14/24

ReduceFrac

a/b=.a /2./.b /2.

- 14÷ 2/24÷ 2

Calculate quotient

- 7/12

Let's analyze the given expression. (- 4/5)^2-3/50 To simplify the expression, we need to start by calculating the power by using the Power of a Quotient Law.

(- 4/5)^2-3/50

NegBaseToPosBase

(- a)^2=a^2

(4/5)^2-3/50

PowQuot

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

4^2/5^2-3/50

Calculate power

16/25-3/50

Now let's perform the subtraction and write the result in simplest form.

16/25-3/50

a/b=a * 2/b * 2

16* 2/25* 2-3/50

32/50-3/50

SubFrac

Subtract fractions

32-3/50

SubTerm

Subtract term

29/50

We are asked to simplify the following expression. (3/10)^2-(- 2/5)^2 According to the Order of Operations, we need to start by calculating the powers. Let's use the Power of a Quotient Law.

(3/10)^2-(- 2/5)^2

NegBaseToPosBase

(- a)^2=a^2

(3/10)^2-( 2/5)^2

PowQuot

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

3^2/10^2-2^2/5^2

Calculate power

9/100-4/25

Now let's subtract the fractions.

9/100-4/25

a/b=a * 4/b * 4

9/100-4* 4/25* 4

9/100-16/100

SubFrac

Subtract fractions

9-16/100

SubTerm

Subtract term

- 7/100

MoveNegNumToFrac

Put minus sign in front of fraction

- 7/100

Let's consider the given expression. 8^2( - 7/8 ) -1/2 According to the Order of Operations, to simplify the expression, we need to start by calculating the power. Then, we will perform the multiplication and subtraction.

8^2( - 7/8 ) -1/2

Calculate power

64( - 7/8 ) -1/2

MultPosNeg

a(- b)=- a * b

- 64( 7/8 ) -1/2

MoveLeftFacToNum

a*b/c= a* b/c

- ( 64* 7/8 ) -1/2