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3sqrt64/27^⅓ - simplify

can you do step by step pls

7 answers

Sure! Let's simplify the expression step by step:

\[ \frac{3\sqrt{64}}{27^{1/3}} \]

Step 1: Simplify \(\sqrt{64}\)

The square root of 64 is 8, because \(8 \times 8 = 64\).

Now, we can rewrite the expression:

\[ \frac{3 \cdot 8}{27^{1/3}} \]

Step 2: Multiply the numerator

Now, multiply \(3\) by \(8\):

\[ 3 \cdot 8 = 24 \]

So, the expression becomes:

\[ \frac{24}{27^{1/3}} \]

Step 3: Simplify \(27^{1/3}\)

Now we need to simplify \(27^{1/3}\). The cube root of 27 is 3, because \(3 \times 3 \times 3 = 27\).

Thus, we can rewrite the expression:

\[ \frac{24}{3} \]

Step 4: Simplify the fraction

Now, we simplify the fraction \(\frac{24}{3}\):

\[ 24 \div 3 = 8 \]

Final Answer

Thus, the simplified form of the original expression \(\frac{3\sqrt{64}}{27^{1/3}}\) is:

\[ 8 \]

Make everything smaller

Sure! Let's simplify the expression \(\frac{3\sqrt{64}}{27^{1/3}}\) using smaller numbers when possible.

Step 1: Simplify \(\sqrt{64}\)

\(\sqrt{64} = 8\)

Step 2: Rewrite the expression

Now, substituting that back in:

\[ \frac{3 \cdot 8}{27^{1/3}} \]

Step 3: Multiply the numerator

Now, multiply:

\[ 3 \cdot 8 = 24 \]

So the expression becomes:

\[ \frac{24}{27^{1/3}} \]

Step 4: Simplify \(27^{1/3}\)

Next, we simplify \(27^{1/3}\):

\[ 27^{1/3} = 3 \]

Step 5: Rewrite the expression

So we can rewrite the expression now as:

\[ \frac{24}{3} \]

Step 6: Simplify the fraction

Now we simplify \(\frac{24}{3}\):

\[ 24 \div 3 = 8 \]

Final Answer

The simplified form of \(\frac{3\sqrt{64}}{27^{1/3}}\) remains:

\[ 8 \]

If you mean to present smaller numbers or different simplifications (like factoring, or using smaller values in other contexts), please clarify further!

( 4√8 ) ^-24 X ( √8 ) ^16 simplify and show all steps

Let's simplify the expression \((4\sqrt{8})^{-24} \times (\sqrt{8})^{16}\) step by step.

Step 1: Simplify \(\sqrt{8}\)

The square root of 8 can be simplified:

\[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \]

Step 2: Substitute \(\sqrt{8}\) into the expression

Now we can substitute \(\sqrt{8}\) with \(2\sqrt{2}\):

\[ (4\sqrt{8})^{-24} \times (\sqrt{8})^{16} = (4(2\sqrt{2}))^{-24} \times (2\sqrt{2})^{16} \]

Step 3: Simplify \(4\sqrt{8}\)

Now we simplify \(4(2\sqrt{2})\):

\[ 4\sqrt{8} = 4 \cdot 2\sqrt{2} = 8\sqrt{2} \]

Now we can rewrite the expression:

\[ (8\sqrt{2})^{-24} \times (2\sqrt{2})^{16} \]

Step 4: Simplifying \((8\sqrt{2})^{-24}\)

Now let's handle the \((8\sqrt{2})^{-24}\):

\[ (8\sqrt{2})^{-24} = 8^{-24}(\sqrt{2})^{-24} = 8^{-24} \cdot (2^{1/2})^{-24} = 8^{-24} \cdot 2^{-12} \]

Since \(8 = 2^3\), we can further simplify:

\[ (2^3)^{-24} = 2^{-72} \]

So:

\[ (8\sqrt{2})^{-24} = 2^{-72} \cdot 2^{-12} = 2^{-72 - 12} = 2^{-84} \]

Step 5: Simplifying \((2\sqrt{2})^{16}\)

Now let's simplify \((2\sqrt{2})^{16}\):

\[ (2\sqrt{2})^{16} = (2(2^{1/2}))^{16} = (2^{1 + 1/2})^{16} = (2^{3/2})^{16} = 2^{(3/2) \cdot 16} = 2^{24} \]

Step 6: Combine the results

Now we have:

\[ (4\sqrt{8})^{-24} \times (\sqrt{8})^{16} = 2^{-84} \times 2^{24} \]

Combine the exponents:

\[ 2^{-84 + 24} = 2^{-60} \]

Final Answer

So the simplified expression is:

\[ \frac{1}{2^{60}} \quad \text{or} \quad 2^{-60} \]

same with this one pls (7^-4 x 7^3)/√49

Let's simplify the expression \(\frac{7^{-4} \times 7^{3}}{\sqrt{49}}\) step by step.

Step 1: Simplify \(\sqrt{49}\)

The square root of 49 is:

\[ \sqrt{49} = 7 \]

Step 2: Rewrite the expression

Now, substitute \(\sqrt{49}\) with \(7\):

\[ \frac{7^{-4} \times 7^{3}}{7} \]

Step 3: Simplify the numerator

Using the property of exponents, \(a^m \times a^n = a^{m+n}\):

\[ 7^{-4} \times 7^{3} = 7^{-4 + 3} = 7^{-1} \]

Step 4: Rewrite the fraction

Now the expression becomes:

\[ \frac{7^{-1}}{7} \]

Step 5: Simplify the fraction

Again, using the property of exponents, we can express the denominator \(7\) as \(7^{1}\):

\[ \frac{7^{-1}}{7^{1}} = 7^{-1 - 1} = 7^{-2} \]

Step 6: Final Answer

Thus, the simplified form of the original expression \(\frac{7^{-4} \times 7^{3}}{\sqrt{49}}\) is:

\[ 7^{-2} \quad \text{or} \quad \frac{1}{7^2} = \frac{1}{49} \]