(8^8)^3
To solve (8^8)^3, we need to apply the exponentiation rules.
First, we solve the exponent inside the parentheses:
8^8 = 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 = 16,777,216.
Now, we raise this result to the power of 3:
(8^8)^3 = 16,777,216^3 = 4,973,686,472,081,026,816.
Therefore, (8^8)^3 equals 4,973,686,472,081,026,816.
please simplify that
To simplify (8^8)^3, we can apply the exponentiation rule which states that raising an exponent to another exponent is equivalent to multiplying the exponents.
Therefore, (8^8)^3 simplifies to 8^(8*3).
Now, we can multiply the exponents: 8*3 = 24.
So, (8^8)^3 simplifies to 8^24.
4^−2⋅4⋅4^−4=
To simplify the expression 4^(-2) ⋅ 4 ⋅ 4^(-4), we'll use the rules of exponents.
Recall that a negative exponent can be rewritten as the reciprocal of the number raised to the positive exponent. Hence, 4^(-2) = 1/4^2 and 4^(-4) = 1/4^4.
Now, we can substitute these values back into the expression:
(1/4^2) ⋅ 4 ⋅ (1/4^4)
Next, we simplify the exponents:
(1/16) ⋅ 4 ⋅ (1/256)
Multiply the numbers:
1/16 ⋅ 4/1 ⋅ 1/256 = (4/16) ⋅ (1/256)
Reduce fractions if possible:
1/4 ⋅ 1/256
Multiply the numbers:
1/1024
Therefore, 4^(-2) ⋅ 4 ⋅ 4^(-4) simplifies to 1/1024.
fully simplify that please
To fully simplify 4^(-2) ⋅ 4 ⋅ 4^(-4), we can apply the rules of exponents.
Recall that a negative exponent can be rewritten as the reciprocal of the number raised to the positive exponent. Thus, 4^(-2) = 1/4^2 and 4^(-4) = 1/4^4.
Now, we substitute these values back into the expression:
(1/4^2) ⋅ 4 ⋅ (1/4^4)
Next, we simplify the exponents:
(1/16) ⋅ 4 ⋅ (1/256)
We can multiply the numbers:
1/16 × 4 × 1/256 = 1/(16 × 256)
Further simplifying:
1/(4,096)
Therefore, 4^(-2) ⋅ 4 ⋅ 4^(-4) simplified to 1/4,096.
fully simplfy
\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}
To fully simplify the expression (1/5) ⋅ (1/5) ⋅ (1/5) ⋅ (1/5), we can multiply the numerators and the denominators together:
Numerator: 1 ⋅ 1 ⋅ 1 ⋅ 1 = 1
Denominator: 5 ⋅ 5 ⋅ 5 ⋅ 5 = 625
Therefore, (1/5) ⋅ (1/5) ⋅ (1/5) ⋅ (1/5) simplifies to 1/625.