Equivalent Exponential Expressions​ 6.3.5

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Upcoming:

3/18 - Assignment

3/23 - Unit Test

Equivalent Exponential Expressions​

By Ashley Moser

• describe the values that result from evaluating expressions with fractions that have exponents

• interpret whether a given value is a solution to an equation that includes an exponent

• evaluate expressions that have a variable, an exponent, and one other operation for a given value of the variable, carrying out the operations in the conventional order

​Recall, when you are given a value for a variable, that value can replace the variable in an expression, as shown in the examples.

Labelling

Complete the table.

Drag labels to their correct position on the image

3

27

9

81

​Examples

Multiple Choice

Which of the following expressions is equivalent to $$5x^2$$ ?

• $$5\cdot x^2$$

• $$5+x^2$$

• $$\frac{5}{x^2}$$

Match

Evaluate each expression for the given value of x.

• $$3x^{2}$$ when $$x=\frac{1}{9}$$

• $$\frac{x^3}{4}$$ when $$x=4$$

• $$\frac{x^3}{4}$$ when $$x=\frac{1}{2}$$

• $$\frac{1}{27}$$

• $$16$$

• $$\frac{1}{32}$$

Match

Evaluate each expression for the given value of x.

• $$9+x^7$$ when $$x=1$$

• $$3x^2$$ when $$x=10$$

• $$9+x^7$$ when $$x\ =\ \frac{1}{2}$$

• $$10$$

• $$300$$

• $$9\ \frac{1}{128}$$

Sometimes expressions have more than one variable and multiple operations. In these cases, you can follow the same steps as the examples you have already completed. Read through an example with multiple variables and operations below.

Multiple Choice

What is the value of $$2x^3+y$$ when x=3 and y=10?

• 74

• 64

• 226

Multiple Choice

What is the value of x in the equation $$64=x^2$$ ?

Look at the choices below and plug them into the variable.

• $$x=\frac{1}{8}$$

• $$x=8$$

• $$x=\frac{1}{4}$$

Match

Match each solution to the corresponding equation.

• $$64=x^3$$

• $$2^x=32$$

• $$2\cdot2^5=2^x$$

• $$x=\left(\frac{2}{5}\right)^3$$

• $$\frac{16}{9}=x^2$$

4

5

6

• 4

• 5

• 6

• $$\frac{8}{125}$$

• $$\frac{4}{3}$$

Match

Match each equation to a solution.

• $$2^x=64$$

• $$x=\left(\frac{2}{5}\right)^3$$

• $$3\cdot\left(3^4\right)=3^x$$

• $$\frac{16}{25}=x^2$$

6

5

• 6

• $$\frac{8}{125}$$

• 5

• $$\frac{4}{5}$$

Draw

Evaluate the expression, $$3x^2+y$$ when x=5 and y=3.

Show your work.

Match

Evaluate each expression for the given value of the variable. Then, match each expression to the correct value of the solution.

• $$2+x^3$$ when x=3

• $$x^2$$ when $$x=\frac{1}{2}$$

• $$10y+x^2$$ when x=6 and y=4

29

76

• 29

• $$\frac{1}{4}$$

• 76

Multiple Choice

Out of the given choices, what is the solution to $$7+x^2=16$$

• x=2

• x=3

• x=4