Question

Instructions: Apply Laws of Exponents to write an equivalent algebraic expression for each given expression.

Question:
`(81t^(8) )/(u^(20) )` (81 times t^8 over u^20

Answer 1

Explanation:

To write an equivalent algebraic expression for

81

�

8

/

�

20

81t

8

/u

20

using the laws of exponents, we can use the following rules:

�

�

/

�

�

=

�

�

−

�

a

m

/a

n

=a

m−n

(When you divide two terms with the same base, subtract the exponents.)

�

−

�

=

1

/

�

�

a

−n

=1/a

n

(A negative exponent indicates taking the reciprocal of the base raised to the positive exponent.)

Applying these rules to the expression

81

�

8

/

�

20

81t

8

/u

20

:

81

�

8

�

20

=

3

4

⋅

(

�

4

)

2

(

�

10

)

2

u

20

81t

8

​

=

(u

10

)

2

3

4

⋅(t

4

)

2

​

Now, using rule 1, we subtract the exponents inside the parentheses:

3

4

⋅

(

�

4

)

2

=

3

4

⋅

�

4

⋅

2

3

4

⋅(t

4

)

2

=3

4

⋅t

4⋅2

Simplify the exponents:

3

4

⋅

�

8

3

4

⋅t

8

So, the equivalent algebraic expression is

3

4

⋅

�

8

3

4

⋅t

8

.

Answer 2

Answer:To write an equivalent algebraic expression using the laws of exponents, let's break down the expression step by step.

The expression is:

\(81 \times \frac{t^8}{u^{20}}\)

First, let's simplify \(81\) using the fact that \(81 = 3^4\):

\(3^4 \times \frac{t^8}{u^{20}}\)

Next, let's use the properties of exponents to combine the terms:

\(3^{4} \times t^{8} \times u^{-20}\)

Now, using the product of powers rule (\(a^m \times a^n = a^{m+n}\)), we can combine the \(t\) terms:

\(3^{4} \times t^{8-20} \times u^{-20}\)

\(3^{4} \times t^{-12} \times u^{-20}\)

Finally, if you'd like, you can write \(3^4\) as \(81\):

\(81 \times t^{-12} \times u^{-20}\)

Explanation:

So, the equivalent algebraic expression using the laws of exponents is \(81 \times t^{-12} \times u^{-20}\).

Hope this helped :)