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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Applying Properties of Exponents In Exercises 1 and 2, use the properties of exponents to simplify each expression.

(a) ( 4 5 ) ( 4 2 )

(b) ( 7 3 ) 3

(c) 2 4

(d) 9 8 9 6

(a)

To determine

To calculate: The value of the expression (45)(42) using the properties of exponents.

Answer

Solution:

The value of the expression (45)(42) is 16384.

Explanation

Given Information:

The provided expression is (45)(42).

Formula used:

Property of exponents:

For any real number x and y,

axay=ax+y

Calculation:

Consider the provided expression, (45)(42)

Here, the base of the expression is the same for two exponents that is 4.

Evaluate the value of expression by applying product rule.

(45)(42)=45+2=47=16384

Thus, the value of the expression (45)(42) is 16384.

(b)

To determine

To calculate: The value of the expression (73)3 using the properties of exponents.

Answer

Solution:

The value of the expression (73)3 is 40,353,607.

Explanation

Given Information:

The provided expression is (73)3.

Formula used:

If the expression is in the form of (xa)b, then the power rule of exponents is given by,

(xa)b=(x)ab

Calculation:

Consider the provided expression, (73)3

Evaluate the value of expression by applying power rule.

(73)3=733=79=40353607

Thus, the value of the expression (73)3 is 40,353,607.

(c)

To determine

To calculate: The value of the expression (2)4 using the properties of exponents.

Answer

Solution:

The value of the expression (2)4 is 0.0625.

Explanation

Given Information:

The provided expression is (2)4.

Formula used:

If the expression is in the form of 1ax, then the negative rule of exponents defines that the negative power in the denominator moved to the numerator and become positive exponent which is given by,

1ax=ax

Calculation:

Consider the provided expression, (2)4

Evaluate the value of expression by applying negative exponent rule.

(2)4=124=116=0.0625

Thus, the value of the expression (2)4 is 0.0625.

(d)

To determine

To calculate: The value of the expression 9896 using the properties of exponents.

Answer

Solution:

The value of the expression 9896 is 81.

Explanation

Given Information:

The provided expression is 9896.

Formula used:

If the expression is in the form of axay, then the quotient rule of exponents defines that if the two exponents are divided with the same base, then the powers are subtracted, and is given by.

axay=axy

Calculation:

Consider the provided expression, 9896

Evaluate the value of expression by applying quotient rule.

9896=986=92=81

Thus, the value of the expression is 81.

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