# Simplify: #{(6^6)^4 -: (6^7)^0 xx[(6^2)^3]^2}^2 -: {[(6^3)^5xx(6^2)^3]^3 : [(6^3)^3]^4}^2#?

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To simplify the expression, we'll start by evaluating the exponents within each set of parentheses:

(6^6)^4 = 6^(6*4) = 6^24

(6^7)^0 = 6^(7*0) = 6^0 = 1

(6^2)^3 = 6^(2*3) = 6^6

[(6^2)^3]^2 = (6^6)^2 = 6^(6*2) = 6^12

Now, let's substitute these values back into the original expression:

{6^24 ÷ 1 ×× 6^12}^2 ÷ {[(6^3)^5 ×× 6^6]^3 ÷ [(6^3)^3]^4}^2

This simplifies to:

{6^24 ×× 6^12}^2 ÷ {[6^(3*5) ×× 6^6]^3 ÷ [6^(3*3)]^4}^2

{6^36}^2 ÷ {[6^15 ×× 6^6]^3 ÷ 6^12}^2

Now, we'll simplify the expressions within the brackets:

{6^72} ÷ {[6^21]^3 ÷ 6^12}^2

Now, we'll simplify the expression within the square brackets:

{6^72} ÷ {[6^(21*3) ÷ 6^12]}^2

{6^72} ÷ {[6^63 ÷ 6^12]}^2

{6^72} ÷ {6^(63-12)}^2

{6^72} ÷ 6^51^2

{6^72} ÷ 6^102

Now, subtract the exponents:

6^(72-102) = 6^-30

Thus, the simplified expression is 1/(6^30).

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To simplify the expression, follow the order of operations (PEMDAS/BODMAS) which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, simplify the expressions within the parentheses/brackets and exponents:

- ((6^6)^4 = 6^{6 \times 4} = 6^{24})
- ((6^7)^0 = 1) (Any non-zero number raised to the power of 0 equals 1)
- ((6^2)^3 = 6^{2 \times 3} = 6^6)
- (6^6 = 46656)
- (6^3 = 216)

Now, substitute these values back into the original expression:

[\frac{{46656^2}}{{(1 \times [6^6]^2)}} \div \frac{{(216^5 \times 46656)}}{{(46656^3 \times 216^3)^2}}]

Now, perform the operations within the brackets:

- ([6^6]^2 = 46656)
- (216^5 = 2,176,782,336)
- (46656^3 = 89,916,082,944)
- (216^3 = 10,077,696)

Now, substitute these values back into the expression:

[\frac{{46656^2}}{{(1 \times 46656)}} \div \frac{{(2,176,782,336 \times 46656)}}{{(89,916,082,944 \times 10,077,696)^2}}]

Now, perform the remaining operations:

- (46656^2 = 2,176,782,336)
- (1 \times 46656 = 46656)
- (89,916,082,944 \times 10,077,696 = 906,573,791,866,017,024)
- ((906,573,791,866,017,024)^2 = 82,045,248)

Now, perform the division:

[\frac{{2,176,782,336}}{{46656}} \div \frac{{2,176,782,336 \times 46656}}{{82,045,248}}]

Now, perform the division:

[\frac{{46656}}{{46656}} \div \frac{{2,176,782,336 \times 46656}}{{82,045,248}}]

[\frac{{1}}{{1}} \div \frac{{101,551,978,898,622,976}}{{82,045,248}}]

[\frac{{82,045,248}}{{101,551,978,898,622,976}}]

Therefore, the simplified expression is approximately (8.0813565 \times 10^{-13}).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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