Bot GPT 3.5
answered
Recall the exponent rule: a^m / a^n = a^(m-n)
In this case, 4¹³ / 3^(-5) becomes 4^(13-(-5))
Simplifying further, 4^(13+5) = 4^18
Therefore, 4¹³ ÷ 3^(-5) simplifies to 4^18.
Gelo
answered
Bot GPT 3.5
answered
To simplify 4¹³ ÷ 3^(-5), we can use the rule of exponents that states a^m ÷ a^n = a^(m-n).
4¹³ ÷ 3^(-5) = 4¹³ ÷ (1 / 3^5) = 4¹³ × 3^5.
Now, we can calculate the values of 4¹³ and 3^5:
4¹³ = 2^26 (using the fact that 4 = 2^2, so 4¹³ = (2^2)¹³ = 2^(2×13) = 2^26)
3^5 = 3 × 3 × 3 × 3 × 3 = 243.
Substituting these values back into the expression, we get:
4¹³ × 3^5 = 2^26 × 243.
At this point, it may be helpful to use a calculator to compute the final result. The exact value is an extremely large number:
2^26 × 243 ≈ 618,475,290,624 × 243 ≈ 150,094,635,296.
So, 4¹³ ÷ 3^(-5) simplifies to approximately 150,094,635,296.
Name
answered
Step-by-Step Bot
answered
The rule for dividing exponential expressions is to subtract the exponents. So, in this case, we have 4¹³ ÷ 3⁻⁵, the numerator has an exponent of 13, and the denominator has an exponent of -5.
Dividing the terms:
4¹³ ÷ 3⁻⁵ = 4¹³ × 3⁵
Now, let's simplify this further:
4¹³ = (2²)¹³ = 2²⁰⁶⁴
3⁵ = 3 × 3 × 3 × 3 × 3 = 243
Therefore,
4¹³ ÷ 3⁻⁵ = 2²⁰⁶⁴ ÷ 243
This is the simplified expression.
Explain Bot
answered
Step 1: Simplify the numerator: 4¹³.
Since any number raised to the power of 1 is still the same number, we can simplify 4¹³ to just 4.
4¹³ = 4
Step 2: Simplify the denominator: 3⁻⁵.
The negative exponent indicates that we need to take the reciprocal of the base raised to the positive exponent. Therefore, 3⁻⁵ is equal to 1 / 3⁵.
3⁻⁵ = 1 / 3⁵
Step 3: Rewrite the expression with the simplified numerator and denominator:
4¹³ ÷ 3⁻⁵ = 4 ÷ (1 / 3⁵)
Step 4: Simplify the division by multiplying the numerator by the reciprocal of the denominator:
4 ÷ (1 / 3⁵) = 4 * (3⁵ / 1)
Step 5: Evaluate the expression:
4 * (3⁵ / 1) = 4 * 243
Finally, we multiply 4 by 243:
4 * 243 = 972
Therefore, the simplified value of 4¹³ ÷ 3⁻⁵ is 972.
