What is \(\frac{1}{3}\) to the tenth power in fraction form?
And what is \((\frac{1}{3})^{10} \times 9^4\)?
Calculate \(\frac{1}{3}\) to the tenth power times 9 to the 4th power.
Answer (3)
Well, 1/3 to the 10th power. Since the numerator is 1, just ignore that.
Find the tenth power of 3. 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 59049 So, 1/3 to the 10th power is equal to 1/59049. 3 1 10 = 59049 1
Okay, for the second equation we know that 1/3 to the tenth power is already 1/59049.
Now find the 4th power for 9.
9 x 9 x 9 x 9 = 6561 9 ∗ 9 ∗ 9 ∗ 9 = 6561
Convert 6561 into a fraction, which is 6561/1.
Now multiply.
1/59049 x 6561/1 = 6561/59049
That fraction reduces into 1/9.
Answer #1: 1/59049 Answer #2: 1/9
1/3 ^ 10 = 1/3 * itself ten times. 1/59049 x 9 ^ 4 1/59049 x 6561 = 6561/59049 ** 1/9**
The value of ( 3 1 ) 10 in fraction form is 59049 1 . The product of ( 3 1 ) 10 × 9 4 simplifies to 9 1 .
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