1. Simplify
26 ⋅ 26^8
2. Simplify
(-5)^5 / (-5)^-6
3. Simplify
8^15 ÷ 8^-3
When the bases are the same...
for MULTIPLICATION add the exponents
for DIVISION subtract the exponents when the bases are the same.
1. 26^1 * 26^8 = 26^9.
2. (-5)^5/(-5)^-6 = (-5)^11.
Note: I subtracted the exponent in the denominator from
the exponent in numerator.
3. Same procedure as #2.
1. To simplify the expression 26 × 26^8, we can use the exponent rule that states: a^m × a^n = a^(m+n). Here, we have 26 × 26^8, which can be rewritten as 26^1 × 26^8.
Applying the exponent rule, we add the exponents, so we get 26^(1+8) = 26^9.
Therefore, the simplified form of 26 × 26^8 is 26^9.
2. To simplify the expression (-5)^5 / (-5)^-6, we can use the exponent rule that states: a^m / a^n = a^(m-n). Here, we have (-5)^5 / (-5)^(-6), which can be rewritten as (-5)^5 × (-5)^(-(-6)).
Now, we need to simplify the second term in the expression, (-5)^(-(-6)). The rule (-a)^(-b) is equal to 1 / (-a)^b. Applying this rule, we have (-5)^(-(-6)) = 1 / (-5)^6.
Therefore, our expression becomes (-5)^5 × 1 / (-5)^6.
Using another exponent rule, (-a)^m = a^m, we can rewrite the expression as (-5)^5 × 1 / 5^6.
Now, we can compute the values: (-5)^5 = -5 × -5 × -5 × -5 × -5 = -3125 and 5^6 = 5 × 5 × 5 × 5 × 5 × 5 = 15625.
Therefore, the expression simplifies to -3125 / 15625 = -1/5.
So, the simplified form of (-5)^5 / (-5)^-6 is -1/5.
3. To simplify the expression 8^15 ÷ 8^-3, we can use the exponent rule a^m ÷ a^n = a^(m-n). Here, we have 8^15 ÷ 8^-3, which can be rewritten as 8^15 × 8^3.
Applying the exponent rule, we subtract the exponents, so we get 8^(15-3) = 8^12.
Therefore, the simplified form of 8^15 ÷ 8^-3 is 8^12.