What is the pattern in the values as the exponents increase?
Powers of 3
Value
3 Superscript negative 1
One-third
3 Superscript 0
1
3 Superscript 1
3
3 squared
9
add 3 to the previous value
subtract 3 from the previous value
divide the previous value by 3
multiply the previous value by 3
The pattern in the values as the exponents increase is that each value can be obtained by multiplying the previous value by 3.
Tasha used the pattern in the table to find the value of 4 Superscript negative 4.
Powers of 4
Value
4 squared
16
4 Superscript 1
4
4 Superscript 0
1
4 Superscript negative 1
One-fourth
4 Superscript negative 2
StartFraction 1 Over 16 EndFraction
She used these steps.
Step 1 Find a pattern in the table.
The pattern is to divide the previous value by 4 when the exponent decreases by 1.
Step 2 Find the value of 4 Superscript negative 3.
4 Superscript negative 3 = StartFraction 1 Over 16 EndFraction divided by 4 = StartFraction 1 Over 16 EndFraction times one-fourth = StartFraction 1 Over 64 EndFraction
Step 3 Find the value of 4 Superscript negative 4.
4 Superscript negative 4 = StartFraction 1 Over 64 EndFraction divided by 4 = StartFraction 1 Over 64 EndFraction times one-fourth = StartFraction 1 Over 256 EndFraction
Step 4 Rewrite the value for 4 Superscript negative 4.
StartFraction 1 Over 256 EndFraction = negative StartFraction 1 Over 4 Superscript negative 4 EndFraction
In which step did Tasha make the first error?
Step 1
Step 2
Step 3
Step 4
Mark this and return
Tasha made the first error in Step 3 when finding the value of 4 Superscript negative 4. Instead of multiplying StartFraction 1 Over 64 EndFraction by one-fourth, she should have divided it by four.
In this sequence, the pattern in the values as the exponents increase can be described as follows:
To find the next value, you can:
- For each subsequent exponent, add 3 to the previous value.
- For each previous exponent, subtract 3 from the previous value.
- For exponents that increase by 1 each time (such as 1, 2, 3), multiply the previous value by 3.
- For exponents that decrease by 1 each time (such as -1, 0), divide the previous value by 3.
By following these rules, you can generate the values in the sequence.