Free Printable GAT

1.

Simplify to an equivalent expression BUT leave in exponent form.
4³⋅4⁵

a)

4⁸

b)

16⁸

c)

4¹⁵

d)

16¹⁵

2.

evaluate ∛64

a)

-4

b)

4

c)

21.333

d)

-21.3333

3.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

4.

Evaluate using the quotient rule:

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

5.

Simplify using the product rule: x³y²x³=

a)

x⁶y²

b)

xy⁸

c)

x³y⁵

6.

Using exponents, simplify the following expression:

(f^-6)(f¹⁰)

a)

f¹⁶

b)

f⁴

c)

1/f⁴

d)

1/f¹⁶

7.

Rewrite using positive exponents

a)

2⁴

b)

1/2⁴

c)

4²

d)

1/4²

8.

Using exponents, simplify the following expression

a)

x^-7

b)

1/x⁷

c)

x⁷

d)

x^-9

9.

Which two exponent rules do you need to use to simplify this expression?

a)

Product Rule and Quotient Rule

b)

Power Rule and Negative Exponent Rule

c)

Power Rule and Product Rule

d)

Zero Rule and Power Rule

10.

Solve for x:

\ x^{\frac{3}{2}}=125

a)

x = 25

b)

x = -25

c)

x = 5

d)

x = -5

11.

Solve for x:

26=-1+\left(27x\right)^{\frac{3}{4}}

a)

x = 27

b)

x = -3

c)

x = 81

d)

x = 3

12.

Solve for x:

-6\ =\ 10-\left(x-10\right)^{\frac{4}{3}}

a)

x = 2

b)

x = 18

c)

x = 2 and x = 18

d)

x = -2 and x = -18

13.

Solve for x:

\sqrt{2x-4}=\sqrt{x}

a)

x = 4

b)

x = -4

c)

x = 2

d)

x = -2

14.

Solve for x:
$-2\ =\ -5+\sqrt{x+7}$

a)

x = 2

b)

x = -2

c)

x = 4

d)

x = -4

15.

Solve for x:
$\sqrt{x-6}=\sqrt{36-2x}$

a)

x = 14

b)

x = -14

c)

x = 6

d)

x = -6

16.

$4+\sqrt{\frac{x}{9}}=5$

Solve for x:

a)

x = -9

b)

x = 9

c)

x = 21

d)

x = -21

17.

$x\ =\ \sqrt{12-x}$

Solve for x:

a)

x = -3

b)

x = 0

c)

x = 2

d)

x = 3

18.

Solve for n:

a)

n = 36

b)

n = 18

c)

n = -18

d)

n = 27

19.

a)

2

b)

-2

c)

4

d)

-4

20.

a)

14

b)

-14

c)

6

d)

-6

21.

Solve:
$x^{3\ }+\ 5\ =\ 13$

(a)

22.

Solve:
$2x^5\ +\ 12\ =-52\$

(a)

23.

x²=25

a)

x = 5

b)

x = -5

c)

x = ±25

d)

x = ±5

GAT

Total questions: 23

Worksheet time: 3hrs 55mins

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