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## Roots Of Exponential Expressions - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=5, Mode=exponent

Find the exponent.

1.
 6  3 24
= 3
2.
 5  4 10
= 4

### Complexity=8, Mode=value

Find the value of the given expression.

1.
 4  5 16
=
2.
 3  7 9
=

### Complexity=8, Mode=variable

Simplify the given expression. Leave out any 1's as coefficients in front of variable expressions. Use '^' to indicate 'to the power of'.

1.
 5  3 15x 45
=
2.
 3  2 12x 27
=

### Complexity=5, Mode=exponent

Find the exponent.

1
 6  3 24
= 3
Solution
 6  3 24
= (324) (1/6) = 3(24 * 1/6) = 3( 24/6) = 34
2
 5  4 10
= 4
Solution
 5  4 10
= (410) (1/5) = 4(10 * 1/5) = 4( 10/5) = 42

### Complexity=8, Mode=value

Find the value of the given expression.

1
 4  5 16
=
Solution
 4  5 16
= (516) (1/4) = 5(16 * 1/4) = 5( 16/4) = 54 = 625
2
 3  7 9
=
Solution
 3  7 9
= (79) (1/3) = 7(9 * 1/3) = 7( 9/3) = 73 = 343

### Complexity=8, Mode=variable

Simplify the given expression. Leave out any 1's as coefficients in front of variable expressions. Use '^' to indicate 'to the power of'.

1
 5  3 15x 45
=
Solution
 5  3 15x 45
= (3 15x 45)(1/5) = 3(15 * 1/5) x(45 * 1/5) = 3(15/5) x(45/5) = 33x9 = 27x 9
2
 3  2 12x 27
=
Solution
 3  2 12x 27
= (2 12x 27)(1/3) = 2(12 * 1/3) x(27 * 1/3) = 2(12/3) x(27/3) = 24x9 = 16x 9